I was wondering at what cruise speed a large jet like the 747 would gain the best distance vs fuel use? For example most passenger cars, 55 - 60mph returns the best mileage for the amount of fuel burnt, but they can go on to do over a 100mph. Would a 747 cruising at M 0.70 burn less fuel on a trans-atlantic crossing than if were doing M 0.86?

Most older airliners had Long Range Cruise performance charts which probably represented nearly optimum fuel efficiency. New ones this information is in the Flight Management Computers and is not directly accessible for the pilots.

LRC had us begin the cruise phase at a slightly higher mach number than we might have selected if we were doing a constant-mach cruise, but slowing down as fuel burns off and the plane gets lighter. Thus we might have, for some specific airplane, begun cruise at M .79 and ended up at top of descent at maybe M .75 or .76

Of course it often also would call for a step climb for longer flights, as going higher when able is always more efficient.

These Cruise charts were wonderfully accurate. The "box" might have shown you your IAS, TAS, EPR or N1, fuel flow, EGT and mach number. Other than the primary power-setting, these were "target values" but were normally right on the money. If the N1 or fuel flow required to give the charted mach number began to increase over time, you might expect that the engines were nearing overhaul.

As great as FMC is, I miss having access to these charts.

Happiness is not seeing another trite Ste. Maarten photo all week long.

Aerodynamics-wise, a particular aircraft's speed for "best mileage" is that which is associated with the point at which a straight line drawn from the origin of the aircraft's thrust-required graph and tangent to its thrust-required curve touches the curve (pardon the mouthful!). That's the maximum-range speed and it is obviously the speed at which you go the farthest. But in addition to going the farthest at that speed, you also maintain the highest distance-flown to fuel-used ratio - in the original poster's words, you get the best "mileage."

This maximum-range speed understandably varies from aircraft to aircraft, and is much slower than you'd think.

It is mostly a question about minimizing the drag. Therefore weight and altitude are the most important factors. The optimum thing is to constantly climb and possibly bleed off a little speed at weight goes does with the fuel burn.

Wind is another very important factor. In headwind you may improve overall fuel consumption by speeding up a little, and visa versa. The navigation system will give you an exact ground speed which can be compared to TAS.

But the real jackpot is knowing the altitude where you have the most favorable wind and have that altitude cleared by ATC.

Always keep your number of landings equal to your number of take-offs, Preben Norholm

Such a rule must be based on some sort of assumption about engine efficiency vs speed, or vs thrust... maybe constant SFC? (Constant with respect to speed, or with respect to thrust?)

But clearly if we want to minimize the work done over a given distance we fly at the speed for minimum drag.

You don't want to minimize drag, minimizing work is the right answer; however, this is not synonymous to minimizing drag. Hence why Qantas332 is correct about the tangent line approximation. This is better than cruising at best L/D (provided there are no drag divergence problems).

This works because jet aircraft are thrust limited systems, vs. power limited for props. The cruise climb maintaining the work minimization scheme is the most efficient cruise (Mach will increase in this mode, so you may hit the drag divergence limit, in which case you move back down the curve to max L/D). Of course ATC won't give you a true cruise climb; however, a the stepped climb gets you almost all of the same benefit.

P.S. On the first order SFC is assumed to be relatively constant, and thrust produced is solely a function of altitude.

"minimizing work is the right answer; however, this is not synonymous to minimizing drag."

It is if you're measuring the two quantities at the same place-- "work" has no other definition. For all I know the tangent-to-the-curve rule works out best in practice, with jet airliners, but it wouldn't necessarily apply with some other kind of engine.

After all, a 747 burns what, maybe 11-12 kg/km in the cruise? Does a tug burn that much, towing the same-weight 747 on level pavement?

It is if you're measuring the two quantities at the same place-- "work" has no other definition. For all I know the tangent-to-the-curve rule works out best in practice, with jet airliners, but it wouldn't necessarily apply with some other kind of engine.

After all, a 747 burns what, maybe 11-12 kg/km in the cruise? Does a tug burn that much, towing the same-weight 747 on level pavement?

Minimizing drag assumes that the only losses are drag based which is not true. The differences are determined by the type of powerplant that is used, be it thrust or power limited. Thrust required (drag) trends with the square of the velocity, but power trends with the cube of velocity. That is why you don't want to fly a thrust limited system at maximum lift/drag (unless MDD is slower than L/D for best range), i.e., min drag (this maximizes endurance but not range). Ideally, with a perfectly ideal jet aircraft and no Mach limit you will fly it at a constant dynamic pressure and a L/D of 0.866 L/Dmax. The reason for doing this is that this is the maximum on the thrust/velocity/range surface.

The tug is power limited, just like prop drive systems are, this indicates that range would be maximized at the minimum drag point. This would not, however, maximize endurance.

Fuel burn is a direct relation to work performed and entropy losses, i.e., system power/efficiency. In powerplants the standard way of measuring fuel consumption is via time. TSFC of PSCF. to move from time to distance you need a velocity.